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Energetics
Training officer(s)
M.LAHOUBI
Stakeholder(s)
M.LAHOUBI
Présentation
Prerequisite
Preparatory classes :
- Partial Differential Equations, Linear Algebra Matrix, Vectors, Determinants, Linear Systems. Green Theorem.
undergraduate cycle :
- Fluid Mechanics EN1, Fluid Mechanics EN2, Heat Transfer EN2
- Partial Differential Equations, Linear Algebra Matrix, Vectors, Determinants, Linear Systems. Green Theorem.
undergraduate cycle :
- Fluid Mechanics EN1, Fluid Mechanics EN2, Heat Transfer EN2
Goal
The aim of this course is to present digital methods as simulation tools and approach methods to engineering issues and decision support.
Presentation
• Introduction to different methods of spatial discretization: finite elements, finite volumes, finite differences, spectral methods. Principles of the methods and their advantages and disadvantages.
• Concepts of precision, convergence, stability. Characteristics of spatial schemes (centred, one-sided) and temporal schemes (explicit/implicit). Limit and initial conditions. Adequate selection of numerical scheme
• Application to a 2D linear system: Heat conduction.
• Approach on non-linear systems: application to Navier-Stokes equations for a viscous, incompressible flow
• Concepts of precision, convergence, stability. Characteristics of spatial schemes (centred, one-sided) and temporal schemes (explicit/implicit). Limit and initial conditions. Adequate selection of numerical scheme
• Application to a 2D linear system: Heat conduction.
• Approach on non-linear systems: application to Navier-Stokes equations for a viscous, incompressible flow
Modalités
Forms of instruction
- Lectures and seminars
- Examples of industrial application of Computational Fluid Dynamics
- Use of CFD Fluent (software)
Organization
| Type | Amount of time | Comment | |
|---|---|---|---|
| Face to face | |||
| Lecture | 8,00 | ||
| Independent study | |||
| Estimated personal study time | 2,00 | ||
| Overall student workload | 10,00 | ||
Evaluation
- 20 hour project: Solving of a problem related to Fluid Mechanics using CFD, realization of geometry and mesh (structured, non-structured), adequate selection of a turbulence model. Analysis and practical use of the results, and physical interpretation (see EN2 TE Simulation fact sheet)
Ressources
Bibliography
Numerical Heat Transfer and Fluid Flow - S. V. Patankar
New York : McGraw-Hill, 1980
Finite Element Procedures in Engineering Analysis - K. J. BatheLondres : Prentice Hall, 1997
Méthode des éléments finis - Une présentation - G. Dhatt, G. TouzotParis : Hermès Science Publications, 2005
Finite Element Programming of the Navier Stokes Equations - C. Taylor, T. C. HuguesSwansea : Pineridge Press, 1981
La Méthode des éléments finis - O. C. ZienkiewiczParis : AFNOR, 2000
Les méthodes d'éléments finis en mécanique des fluides - P. A. RaviartParis : Eyrolles, 1981